Hi
Travelling in Beijing, of couse you should not miss the Great Wall, the Forbidden City, the Temple of Heaven and the Summer palace. I think you could refer to these Beijing Tours(https://www.travelchinaguide.com/package/beijing.htm) , which supply you with Beijing must and visiting itinerary in detail.

You can both buy cheap clothing and electronics in Beijing. For cheap clothing, you may go to Tianle Costumes Wholesale Market at 12, Xiwai Nan Lu, Xicheng District. For cheap electronics, you may go to Zhongguancun.

There seems no pure Vegetarian and Indian Hotels in Beijing. However, there are many vegetarian and Indian restaurants in Beijing. You can find them easily, such as Taj Pavilion (Indian Restaurants) at L128, 1/F, Guomao Mansion (West), No.1, Jianguomenwai Dajie, Chaoyang District; Pure Lotus Vegetarian Restaurant(Vegetarian restaurant) at No.10, Nongzhan Nanli, Chaoyang District.